Outgoing BBC director general Mark Thompson is in talks with the New York Times about becoming its new chief executive to fill the vacancy left after Janet Robinson was fired in December.

Discussions between Thompson and New York Times executives are still active, although it is believed that the 54-year-old Briton is also considering other jobs.

That implies he has not firmly made up his mind what to do after he leaves the broadcaster, which he has helped steer through a change of government and a new licence fee deal. He is due to leave after the London Olympics, once the BBC has appointed a new leader. The corporation is hoping to announce his replacement in July.

A source not connected to Thompson said he had had two meetings in London over the past four weeks about the vacant New York Times Company chief executive role – and that the meetings appeared to be part of a "co-ordinated attempt" by the US newspaper publisher to hire Thompson.

It had been often speculated that Thompson, who currently lives in Oxford, would be keen to work in the US after he left the BBC, because his wife Jane Blumberg is American – although with his children grown up he is open minded about where to live.

The New York Times Company owns the Boston Globe and the International Herald Tribune as well the newspaper from which it takes its name. The company has been under pressure, like other newspaper publishers, in recent years with the decline in the print business, and last year it lost $40m net after turnover fell 3% to $2.3bn.

Although Robinson was forced out in December, in a surprise falling-out with chairman Arthur Sulzberger Jr, the New York Times Company only began the search process in March and signed off on a job description in April. Sulzberger has been interim chief executive since Robinson's departure.

That reflects tensions within the company and its controlling family, amid reports that another member of the Ochs Sulzberger family, Michael Golden, was pursuing the chief executive's job.

Sulzberger is the controlling shareholder at the New York Times Company, and acts both as the chairman of the company and the publisher of the New York Times newspaper – functions that technically rank above and below the chief executive.

Unlike the BBC, whose funding structure dictates that it must be freely available, the New York Times newspaper chose to adopt a metered paywall in an effort to boost digital revenues. The experiment has been relatively successful: the paper had 454,000 digital subscribers at the end of the first quarter of this year.

The New York Times Company declined to comment.

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